

Table REF  gives the specific steps of the proposed algorithm RTEA.
Note that, in this algorithm, the computation of \(r_0\) , \(r_1\)  and \(r_2\)  can be implemented directly with convolution,
and the rest steps are element-wised independent,
where practically multi-threading computation can be directly adopted.
The systematic structure of the proposed RTEA for fault detection of rolling element bearings is presented in Figure REF .
Since this algorithm is derived using MM procedure, the convergence can be guaranteed and converges to the optimal minimizer in this case.
The detailed proof of MM for convex problems can be found in Ref. [1]}.
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